Kinetic Collision Detection for Convex Fat Objects

We design compact and responsive kinetic data structures for detecting collisions between n convex fat objects in 3-dimensional space that can have arbitrary sizes. Our main results are: (i) If the objects are 3-dimensional balls that roll on a plane, then we can detect collisions with a KDS of size O(nlogn) that can handle events in O(log2 n) time. This structure processes O(n2) events in the worst case, assuming that the objects follow constant-degree algebraic trajectories. (ii) If the objects are convex fat 3-dimensional objects of constant complexity that are free-flying in R3, then we can detect collisions with a KDS of O(nlog6 n) size that can handle events in O(log7 n) time. This structure processes O(n2) events in the worst case, assuming that the objects follow constant-degree algebraic trajectories. If the objects have similar sizes then the size of the KDS becomes O(n) and events can be handled in O(logn) time. Keywords Kinetic data structures

• Type: Conference
• Year: 2006
• Where: ESA
• Authors: Mohammad Ali Abam, Mark de Berg, Sheung-Hung Poon, Bettina Speckmann
• Keywords: Algorithms, Constant-degree Algebraic Trajectories, ESA 2006, Fat Objects, Kinetic Data Structures